The invention relates to a device for injection a fuel gas mixture and to a method for producing a device for injecting a fuel-gas mixture. German Patent Application 32 40 554 Al already discloses a device for injecting a fuel-gas mixture in the form of a throttle-pintle fuel injection valve with a cup-shaped gas enveloping sleeve, the injection port of which is surrounded in the immediate vicinity of the gas guide sleeve by an annular gas gap communicating with an annular gas conduit. At least one axially extending, groove-like gas guide conduit that is defined by the circumference of the fuel injection valve, discharges into the annular gas conduit, and which serves to deliver the gas to the injection port of the fuel injection valve is disposed in the cylindrical part of the gas enveloping sleeve. With its inner wall, the cylindrical part of the cup-shaped gas enveloping sleeve rests on the circumference of the fuel injection valve, so that in this way the gas enveloping sleeve is centered relative to the fuel injection valve. This kind of cup-shaped gas enveloping sleeve, with axial gas guide conduits embodied as grooves in the inner wall of the cylindrical part, is complicated in structure and expensive to manufacture. If the functionally necessary exact centering of the gas enveloping sleeve relative to the fuel injection valve is to be assured, then very close manufacturing tolerances must be adhered to, which makes for expensive production.